Current Issue
 Back Issues
 FFC Winery
 Contact Us
 Terms of Use

Vol. 5, No. 3

Zilkowski's Theorem
by Karl Iagnemma

Henderson slipped into the back of the half-full auditorium and settled into an empty chair, shielding his face with a tattered yellow notepad. Around him, mathematicians stood in groups of three and four, sipping coffee from Styrofoam cups and cracking jokes about variational calculus and Zermelo-Fraenkel set theory. Their dreary humor seemed perfectly suited to the auditorium, with its frayed orange carpeting and comfortless chairs and flickering fluorescent lights. So this is Akron, thought Henderson. It was neither better nor worse than he’d expected.
    The conference was the same every year, the same three hundred people, the same dismal cities: Gdansk one year, then Belfast, now Akron. Where next—Mogadishu, perhaps? Teheran? Henderson recognized and disliked many of the faces he saw; he found these people infinitely more agreeable bound between the covers of journals, their moist handshakes and pungent breath eliminated, their grating voices smoothed by the uninflected diction of mathematics. Henderson ducked his head and scribbled idly on his notepad. He did not want any of his colleagues to notice him, but mostly he did not want to catch the eye of the speaker, Czogloz.
    Czogloz was presenting a paper entitled “Perturbation Analysis of Weakly Nonlinear Systems,” and as the clock swept past two o’clock he stepped to the podium and flipped on the overhead projector. He looked younger than Henderson had hoped he would: his hairline was anchored firmly to his temples, and his forehead was free of the frown-shaped wrinkles that marked most mathematicians. Four years of assistant professorship had not affected Czogloz much; this seemed unfair to Henderson. Czogloz was sporting a goatee, and wearing a tie made of some shiny purple material that Henderson thought totally inappropriate for a presentation on weakly nonlinear systems. The goatee, Henderson noted, gave Czogloz a demonic air.
    “Welcome,” Czogloz began, in his lush Hungarian accent, “it’s good to see so many familiar faces.” Henderson instinctively shrank deeper into his chair, but Czogloz was only following his notes; his gaze never left the podium. He launched smoothly into his presentation, first defining the problem with nitpicky precision, then briefly reviewing related research: Dobujinski’s famous 1964 theorem, an obscure series of proofs by a Greek named Kaliardos. Then Czogloz cleared his throat and waded into his own research, his voice rising a half-octave and the words coming faster. Henderson surveyed the dim auditorium: he sensed a grudging respect, a retreat from the skeptical hostility that usually prevailed at the conference. He turned back to the projection screen and began scribbling desperately on his notepad, mentally probing the equations for a tender spot, a place where he could sink a lance.
    Czogloz placed a transparency entitled “Summary and Conclusions” on the overhead projector, and as if awakening from a dream the audience shifted slightly. “So it has been shown,” Czogloz said, “that stability can be analyzed using classical perturbation analysis, provided the system is weakly nonlinear and locally differentiable.” He glanced up from his notes with a reserved but winning smile. “Now. Could I address any—”
    “Question,” Henderson said. His voice held a nervous, aggressive tone, but he didn’t attempt to soften it. He’d been waiting for this moment for so long. “What about the invertibility of the matrix H? You haven’t addressed the case where H is singular.”
    Czogloz peered into the murky reaches of the auditorium. “Could you be more specific, please?”
    “Certainly,” Henderson said. A few faces in the audience glanced back at him. “On transparency eleven, you claim that if the matrix B is positive definite then H is non-singular, but you don’t discuss the case where B is positive semi-definite. And of course it’s possible that, for a dissipative system, B could be positive semi-definite. And thus H could be singular. And thus non-invertible.”
    Czogloz paused. Slowly, he leafed through his transparencies until he reached number eleven. He placed it carefully on the overhead projector, then turned his back to the audience and stared up at the wide white projection screen. A murmur had surfaced in the auditorium, and there was a tautness in the sound that recalled for Henderson a movie dramatization of a public execution. Czogloz unconsciously stroked his goatee, studying the graceful unfolding of the problem, the ingenious substitution that landed it onto solid footing, then the minor but critical assumption Henderson had attacked.
    “Yes, of course.” Czogloz cleared his throat. His ears were glowing as if they’d been badly sunburned. “The condition of positive definiteness can be viewed as a restriction of the method. A limitation.”
    “A limitation? It would seem that your subsequent results are invalidated.”
    Now the auditorium was silent except for the patient hum of the overhead projector fan. Czogloz nodded stiffly. “That may be correct. I’ll have to consider more thoroughly the...implications.”
    An appreciative rumble rose from the audience. This type of drama was rare, and always welcome: it would be recounted in hushed whispers at the next conference, and the next, and the next after that. Henderson would be viewed with a mixture of fear and respect; his own presentations would become targets for mathematical headhunters. Henderson knew this. He also knew there would be a small crowd awaiting him at the end of the presentation, so before Czogloz could clear his throat forcefully enough to regain the audience’s attention, he slipped out the back door.



In his damply air-conditioned Marriott room that evening, as Henderson was packing his garment bag and sipping mini-bar champagne—a reward for his cruel but delicious victory that afternoon—the telephone rang.
    Czogloz’s voice held a cheerful lilt. “Hello, John. I hope I haven’t disturbed you—you sound quite merry.”
    Henderson coughed harshly as champagne fizz tickled the back of his throat. He set the plastic tumbler down and wiped his mouth, his palms suddenly damp with perspiration. “Listen, Miklos: there’s no point in getting worked up.”
    “Oh, no, I’m not worked up,” Czogloz said. “In fact, I must thank you for pointing out my error this afternoon. In the taxi, going back to the hotel, I realized a solution that avoids the difficulty you pointed out. An extraordinary little solution, actually. It could open an entirely new area of research for me.”
    “Well. That’s wonderful.” Henderson stretched the telephone cord into the bathroom and grabbed his shaving kit and toothbrush and stuffed them into the garment bag. “I’m sorry, I can’t talk right now, Czogloz. I’m leaving for the airport.”
    “In an ideal world,” Czogloz continued, “you might have been slightly more... discreet. But there it is.”
    Beneath Czogloz’s accent, Henderson thought he detected an alcohol-induced slur. The thought of Czogloz drunk made Henderson uneasy, and he quickly zipped his bag and scanned the empty room. “Well, I’m off. I’ll see you at the next conference. Or around town, I suppose.” Czogloz and Henderson both taught in Boston—Czogloz at a university downtown and Henderson at a technical college in the suburbs—but Henderson had managed to avoid Czogloz for the past four years.
    “I thought we could meet,” Czogloz said. “In the hotel bar. Shall we say...thirty minutes?”
    “You’re in this hotel?” Henderson glanced nervously at the locked door. “How did you know I was staying here?”
    “John, my goodness—you’re acting like a character in a horror movie. Relax. I’m down the highway, at the Comfort Inn. I’ll buy you a drink—Wild Turkey bourbon, if I remember correctly.”
    “I don’t think so, Czogloz. I’d love to catch up on old times, but I’m flying out at eight-thirty.”
    “There’s a matter we should discuss.” Czogloz’s voice held a dull, melancholy note. It was the voice of a man announcing an unfortunate but inevitable piece of news. “It’s Marya, actually.”
    At the sound of Marya’s name a shiver began in Henderson’s chest that scurried over every inch of his skin. He felt as though he’d been heated over glowing coals and then dunked into an ocean-sized bath of ice water. “What about Marya?”
    Czogloz sighed—a deep, troubling soul-sigh. “Too much. Too much for the telephone.”
    Henderson slumped onto the bed, feeling a familiar ache of yearning and despair, and found himself face-to-face with his reflection in the armoire mirror. He studied the image dispassionately—the frayed hair, the flabby neck and too-small shirt, the nervous, darting tongue that even to Henderson seemed vaguely obscene—then turned slowly away. “Thirty minutes,” he said finally. “I’ll need to change my flight.”
    “Wonderful,” Czogloz said. “Do that, John. Change your flight.”



Henderson crossed the faded lobby of the Marriott Hotel and paused at the entrance of Chez Georges restaurant. Through the smoky glass doors he saw a row of figures hunched at the bar, and toward the far end he thought he spotted Czogloz’s goatee and shiny tie. Henderson rested his hand on the door handle, then backed away and hurried to the men’s room and stood in front of an unoccupied urinal and closed his eyes. His heart was fluttering as though he’d just climbed a dozen flights of stairs. Henderson stood at the urinal, exhaling deeply, until he noticed the man next to him frowning; then he flushed and splashed his face in the sink and marched back across the lobby toward Chez Georges, toward Czogloz.
    Miklos Zoltan Czogloz, from Budapest via Louisville. They’d met as first-year graduate students at the Michigan Engineering Institute, two aggressive young theorists who disagreed about Marx and Irish beer but agreed that mathematics was a game—the most elaborate, wonderful game, like puzzling out riddles posed by God. That first semester, while ninety inches of snow buried the institute, Henderson and Czogloz sat across from each other at the pitted oak tables of the Bachman Library, working increasingly difficult equations until they could solve them without thinking, like concert pianists playing finger exercises. When the semester ended, they moved into the top half of a decaying Dutch colonial on Mill Street, four blocks from the mathematics building. They smashed a six-dollar bottle of Asti Spumante against the brick windowsill and howled into the frozen December night, and Czogloz christened the house Poincaré Manor, in honor of his favorite mathematician.
    And then Henderson met Marya. Marya Zilkowski, from Bialystok, who liked mathematics but didn’t love it, and worried more about whether her kielbasa—which she stuffed by hand, in the bathtub—had too much garlic or black pepper. It was never clear to Henderson why she’d enrolled in graduate school, but he didn’t care; no matter why she’d come, he wanted her to stay. Henderson began avoiding the library and instead lay tangled with Marya in his narrow twin bed, listening to Charles Mingus albums or making strenuous love or sampling Polish recipes that Marya had learned from her babcia. She had a California-shaped birthmark, Henderson discovered; she was prone to irrational fits of laughter; she worried that her luxuriant country accent made her sound rude and unintelligent. Marya was flighty—she made important decisions impulsively, as if she were deciding which pair of socks to wear—and although this frustrated Henderson he envied her ability to change her mind, to implicitly admit she’d been wrong. Marya in the evening would cook enormous platters of kapusta or bigos or pierogi, and Czogloz, returning from the mathematics building at midnight or 1 a.m., would accept a plate of food and sit with Marya and Henderson on the Salvation Army sofa and watch Hogan’s Heroes reruns. Henderson and Czogloz spoke with unabashed optimism of the control-theory problems they would solve—it seemed only a matter of time—while Marya joked about her future restaurant, Mala Warszawa: Little Warsaw, Polish home cooking.
    They lived in Poincaré Manor for two years, and during that third summer Henderson flew to Newark for an adaptive-control conference. Four days without Marya—he sat at the back of over-air-conditioned conference rooms, his blank notebook before him, and found himself imitating Marya’s careless loopy signature. He wrote Marya Henderson, and the sight made him fidgety with excitement. He decided to skip the Friday presentations. It was an uncharacteristically impulsive decision. That Thursday evening at the airport, hurrying through the drab terminal, he felt a sense of supreme gratitude and wonder, the way he imagined Euler must have felt when he realized equaled exactly zero, nothing. His sneakers chirped against the tile floor, a sound that inexplicably brought tears to his eyes. At home, as he worked his key in the deadbolt, he thought he heard something odd—a familiar voice with an unfamiliar inflection—but he put it out of his mind. His hands trembled against the scratched brass lock.
    There was a single terrible moment, when Henderson’s garment bag slumped to the floor and Marya glanced up from the kitchen table. She was wearing a blue gingham apron and beneath it was naked. Czogloz was lying on the sitting-room floor with a plate of golabki beside him and a Journal of American Mathematics propped on his chest, and apart from a pair of red sweatsocks he, too, was naked. Henderson stepped back and pulled the door shut. He stood frozen for a moment—he heard Czogloz’s plate clatter against the pine floorboards, and Marya cried Czekaj! in a strangled, unnatural tone—then Henderson was gone, scrambling down the stairs and across the dark quadrangle, toward the mathematics building and the safety of his empty office.
    Later there was a telephone call, Marya hiccupping through tears and speaking in anxious half-Polish phrases. I am stupid, kochana, I am sorry, she’d said, over and over—but she hadn’t offered to take him back. It was a plain, miserable fact: she loved Henderson but she loved Czogloz more. Flighty, flaky Marya had changed her mind. It wasn’t something that made sense to Henderson, but then nothing that involved women and love had ever made sense to him. He began sleeping in his office, unable to bear the sight of Marya’s bra uncoiled on the floor of Czogloz’s room, the smell of her perfume—Chanel No. 5, a classic and melancholy scent—on Czogloz’s hand towels in the bathroom. That December, when their lease was up, Henderson at midnight stuffed his clothes and textbooks and yellow notepads into eight liquor boxes and loaded them into a taxi, and moved into a studio across the river from the institute. And for the next eighteen months, when he saw Czogloz at a seminar or dissertation defense, they talked about ice hockey or control theory, and did not mention Marya’s name.
    But even now Henderson kept the single remaining relic of his and Marya’s relationship—a pair of pink cotton panties—in the far reaches of his lower-right desk drawer. Some Friday afternoons, when the Evans Building was abandoned and the carillon had tolled its dirge, Henderson found himself closing his office door and leaning back in his armchair, into a slant of sunlight, with the panties crushed up under his chin. Although they’d been washed accidentally, years ago, sometimes Henderson thought he could smell Marya’s eastern-European tang of garlic and dried leaves, her scent. On the back of the panties, near the tag, was a sight that never failed to twist Henderson’s heart: the word MARYA penned in blurry blue ink. He thought he had never seen a name as beautiful or as tragic.



Czogloz, slouched against the bar, did not look as young as he had that afternoon during his presentation. His suit coat was thrown over a stool and his purple tie was loosened, and he wore the look of a traveler stranded overnight in an airport terminal. As Henderson crossed the room, Czogloz rose unsteadily, clutching the bar for support, then shook Henderson’s hand with a slightly feminine grip.
    “Good to see you, Miklos,” Henderson said. “Love your tie.”
    Czogloz grinned wearily. “Hello, John. It’s good to see you, too.” There was a sincerity in his voice that Henderson found disarming. “I read your contraction-analysis paper in the J.A.M. Wonderful work.”
    “Not really,” Henderson said. “A minor observation surrounded by well-known facts. It didn’t deserve publication.”
    This was the truth and they both knew it, but Czogloz shrugged diffidently. He glanced down at the bar and spread his hands, a conciliatory gesture. “I must tell you, I am not angry about this afternoon. For a while, after the presentation—yes, I was somewhat... perturbed. But no more.”
    Czogloz was drinking what looked like cough syrup, and Henderson ordered another and a Wild Turkey for himself. When the drinks arrived, Henderson took a polite sip and said, “So. Marya.”
    “Marya.” Czogloz tilted his glass, watching thick red liquid coat the walls of the tumbler. “We’re finally getting married, in October. I don’t know if you’ve heard.”
    “Hersch told me,” Henderson said. “Congratulations. I wish you every happiness.” His words were dull and lifeless, a parody of congratulations. “How is she?”    
    Czogloz frowned hard into his glass. “She was happy, until a few months ago. She was teaching a Polish-cooking course at the BCAE. We put a down payment on a very nice condominium in the city. And then something happened. She ‘found religion,’ as she likes to say.”
    “My goodness,” Henderson said. “And I have trouble even finding my car keys.”
    “That’s funny,” Czogloz said, without smiling. “I’d almost forgotten about your interesting sense of humor.” Czogloz signaled for another drink and tapped the base of his tumbler against the bar until it arrived. “And now she is carrying things too far—even the priest agrees. She called Krakow last month to tell her mother about the time she stole six hundred thousand zlotys from her grandmother’s purse. The poor woman! Seventy years old, listening to her only daughter tell her she’s a thief.”
    “A conversion,” Henderson mused. “Jesus. Who’d have guessed?” The bourbon was warming him into loquaciousness, and the strangeness of the story warmed him further. He was glad, he reflected, that he’d changed his flight and come tonight. “I suppose it’s nice for her, but how many people is she hurting? Her mother, you. Who else?”
    Czogloz nodded. “I was hoping you could help.”
    “And why would I do that?”
    “For Marya. And for me. It is making things...difficult.”
    Henderson stirred his drink with his pinkie, then licked his finger. “Really? How difficult?”
    Czogloz nodded, as if he’d been expecting the question. “She will no longer go to horror movies, which is something we both—we all—loved. She spends weeknights at Bible study or adoration, then berates me for not attending with her. She’s begun listening to Christian folk music.”
    “That’s it? Movies and shitty music?”
    “She told me last week she was reconsidering the wedding.”
    Henderson paused with the bourbon nearly to his lips, then recovered and took a long, casual sip. He was not completely surprised; it was just like Marya to dither over something so important. Czogloz’s lips were pursed; he was staring at the tall, ornate pepper mill that stood in an alcove behind the bar like a religious icon. “Do you know, John, that Catholics believe Jesus Christ rose from the dead?” Czogloz grinned bemusedly. “That he hopped up, stone dead, and strolled away? Remarkable.”
    Henderson could not imagine Marya kneeling in a church, or praying, or lifting a gaudy gold chalice to her lips; she was so thoroughly carnal. When he thought of Marya, he most often thought of cooking—the tightly rolled gawumpki, the swollen, bursting kielbasa, the thick Bulgarian wine—or he thought of sex.
    Henderson had never been drawn to religion; the notion of a God seemed as abstract to him as nonlinear control theory did to most other people. Some late nights, the sheets in knots and his forehead filmed with sweat, Henderson found himself yearning for some nebulous goodness into which he could cast his irritation and anxiety and self-doubt. In his half-dreaming state he envisioned the faux-antique wishing well that stood in the lobby of the nearby McDonald’s. When he woke the next morning, however, he felt a caustic mixture of skepticism and shame. For what was there to believe in? The ability of people to grow accustomed to even the cruelest discomfort. The dusky accumulation of regret with every passing year. The flow of electrons from low potentials to higher ones. Beyond that—what?
    “There’s more,” Czogloz said. “There’s the matter of her Ph.D.”
    The restaurant’s jazzy music seemed to pause, and the other patrons’ voices fell mute, as though they were speaking through cotton. Henderson watched Czogloz study the empty bottom of his glass. “She wants to give up her Ph.D. And she wants to announce the truth, in the J.A.M.
    Henderson clutched Czogloz’s wrist. “Jesus, Miklos. Stop her.”
    “She’s very serious about it,” Czogloz said, extracting his wrist with a gentle but firm tug. “She says the situation has always made her feel terrible.”
    Henderson slumped against the bar and mechanically signaled for another round. He felt a numbness that went far beyond the effects of the bourbon. He felt like a dental patient dulled by Novocain, indifferently watching the world move before him.
    “You know,” Czogloz said, “I think it’s the best work you’ve ever done. Zilkowski’s Theorem—I knew it wasn’t actually hers. She didn’t care about it, it was nothing to her. And yet...” He trailed off. “Such beauty. A beautiful proof.”
    Henderson shrugged bleakly. “I was inspired, I suppose.”
    “It must have pained you to see it published under someone else’s name.”
    “Not at all,” he said, with more feeling than he’d intended. “I was happy for Marya. I wanted her to be happy.”
    “Happiness.” Czogloz grinned ruefully. “A difficult condition to achieve.”
    It had started five months after Henderson moved out of Poincaré Manor: she’d called one chilly May morning, while Henderson was struggling against the impulse to draw the blinds and stay in bed until noon. Marya’s voice sent a warm shiver down through his thighs. “Are you well?” she’d asked, and it was all he could do not to laugh bitterly. “Perfect,” he’d said, eventually. “How are you?”
    She told him about her mother’s arthritis, about the hot, needling pains in her own wrists, about the pumpkin-colored sweater she’d knitted for her sister’s son, Stefan. Her voice slipped into a languorous drawl, and suddenly it was as if she’d never done the thing she’d done: they talked about Reagan, and Charlie Parker. They talked about sex. She told him details about herself and Czogloz that Henderson could not bear to hear but that thrilled him nonetheless. But there was a problem, she admitted. Her dissertation—she was stuck. The feeling, she explained, was like trying to run a marathon without understanding how even to crawl. “Who knows? Maybe I’ll return home,” she said, with a sigh. “Maybe it’s time to open Mala Warszawa.”
    “Don’t,” Henderson said. “Please don’t. Give me six weeks—a month.”
    Henderson went to the library. Marya was studying a class of problems not too distant from his own research, and within a week he’d discovered some curious connections. That next Sunday, there was a feverish stretch of hours when equations seemed to fall all around him, like ripe fruit from a tree. He scribbled them down as fast as he could write. Monday morning, exhausted, he called Marya’s apartment to tell her the news, but Czogloz answered the phone. Henderson closed his eyes and hung up.
    It happened occasionally: the Ph.D. student who flared like a brilliant comet, then disappeared. Marya’s dissertation committee, after her defense, convened for only seven minutes—seven minutes—then burst from the conference room to tell her she’d passed, that she was now Dr. Marya Zilkowski. And she had not published a single paper since.
    “So,” Czogloz said, setting his empty glass on the bar, “the final reason I called you tonight: Marya and I would like to invite you to dinner next week, at our condominium.”
    The thought of sitting down to dinner between Czogloz and Marya seemed so ludicrous to Henderson that he stared at Czogloz for a long moment without saying anything. “Dinner,” he said finally.
    “Marya’s been experimenting with new recipes—Polish-French, Polish-Cantonese.” Czogloz shrugged. “Fusion cuisine, I suppose.”
    Henderson rose unsteadily from the stool. He felt flustered, and weary. And drunk. “No French,” he said. “No Cantonese—just Polish. Tell her I’ll come only if she cooks plain Polish.”
    Czogloz nodded. “I’ll ask her to make bigos.” He looked up at Henderson with a clear-eyed expression that, for a moment, seemed almost wistful. “It was your favorite, I believe. Yes?”
    “They were all my favorites,” Henderson said.

Go To Page: 1 2
Entire Story

Back to Top

© 2001- American Zoetrope
All trademarks used herein are exclusive property of The Family Coppola